Optimal scale combination selection in generalized multi-scale hybrid decision systems

Abstract

When processing multi-scale hybrid data, the existing methods are insufficient to directly select the optimal scale for different types of data. To deal with this issue, the concept of generalized multi-scale hybrid decision systems (GMHDSs) consisting of numerical, nominal and set-valued values is first introduced. Then, under a scale combination, the information granules of different types of attributes in a GMHDS are constructed and they further fused as the granules of the system. Based on these granules of a given scale combination, positive region and conditional entropy are specified in a GMHDS. To select appropriate single scale systems to keep the positive region and the conditional entropy unchanged for final decision, concepts of positive region optimal scale combinations (POSCs) and conditional entropy optimal scale combinations (CEOSCs) in GMHDSs are defined, respectively. Furthermore, algorithms for calculating a POSC and a CEOSC in a GMHDS are also formulated. Finally, a comparative study of our methods with these based on original data under KNN and NB classifiers is conducted on twelve UCI datasets for the assessment of their classification performance. The experimental results indicate that the proposed methods are of better classification performance than the original data based methods in most cases.